This multicenter, randomized, double-blind, controlled, dose-escalation study will evaluate a humanized monoclonal antibody in patients with chronic refractory immune thrombocytopenic purpura. The antibody alters the ability of T-cells to stimulate B-cells to make autoimmune antibodies. A single 30 min IV infusion will be given to patients with ITP who have failed steroid and splenectomy therapy. Subjects will be randomized to receive escalating doses of antibody based on the results from previous lower doses. Pharmacokinetic data will be recorded as well as platelet counts and levels of anti-platelet antibody, phenotypes of peripheral blood lymphocytes and levels of serum immunoglobulins. Should the antibody prove safe and effective, future trials are planned involving a larger number of subjects.